Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.
同时得到一些关于四元数矩阵的性质，以及体上矩阵相似和合相似的充要条件。
The necessary and sufficient condition for the steady-state output controllability of linear time-invariant systems is presented.
对线性定常单变量系统常值稳态输出的可控性问题进行讨论。
Using this extended quadratic optimization theorem, the necessary and sufficient condition for the existence of stable quadratic optimal closed-loop system is obtained.
利用这个推广的二次最优定理，得到了存在稳定的二次最优闭环系统的充要条件。
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